"Beating bush" is a phrase that means searching for something without any success. There are a number of synonyms you can use that have a similar meaning. For example, you could say that someone is "Looking for a needle in a haystack," "Searching high and low," or "Going on a wild goose chase." Another possibility is to use the phrase "Hunting for something." This implies that the person searching is like a hunter pursuing prey, but still unable to find what they are looking for. No matter what word you choose, remember that it's always good to have a variety of ways to express the same idea.